MathLabs

Problem 2

Prove that if one and only one edge of a tetrahedron is greater than 11, then its volume is at most 18\frac18.
Step 4 of 6: Substitute the bounds
Previous stepNext step
V≤16z(1−z24)V\le\frac16z\left(1-\frac{z^2}{4}\right)
Detailed analysis

Since sin⁡θ≤1\sin\theta\le1, the volume formula yields V≤16z(1−z24)V\le\frac16z\left(1-\frac{z^2}{4}\right).